An Asteroid A, with a mass of 10¹³ kg, is traveling at the velocity of 50 km/s in the positive x-direction and entering the Asteroid Belt. The Asteroid Belt has a width of 10⁶ km. The asteroids in the Asteroid Belt all have masses of about 10¹³ kg each and are traveling with velocities of about 10 km/s in the positive y-direction. Assume that while traversing the Asteroid Belt, Asteroid A is going to collide with at least three other asteroids far apart from each other (it encounters a Family of Asteroids). Assume that all of the collisions happen in the x-y plane and that none of the asteroids are destroyed in the collisions.

Is Asteroid A going to leave the Asteroid Belt? If so, how far off-course in the y-direction (it was originally traveling along the x-axis) is it located when it leaves the Asteroid Belt? How would your answers change if Asteroid A collided with more asteroids?

Make any assumptions you think are reasonable about the collisions and state those assumptions. You can solve the problem analytically or numerically using your favorite software (Matlab, Mathematica, etc.). Graph the trajectory of Asteroid A.

Post your answers to this discussion. After you post your answers, work with your classmates who have already posted to determine the correct answers.

Additional Resources

For this assignment, you will need to calculate the best approach using graphing software. Here are three potential options:

Desmos: This is a free online tool.

• Free MATLAB Trial: "MATLAB Online: may be used with a trial license, though this must be verified through MathWorks upon choosing this option. The benefit of this option is that no software is installed on your system. You access the software through a web browser.
• Free Mathematica Trial: The trial is only for 15 days.